Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 4 | 191

EXAMPLE 4–12 Cooling of an Iron Block by Water

A 50-kg iron block at 80°C is dropped into an insulated tank that contains

0.5 m^3 of liquid water at 25°C. Determine the temperature when thermal

equilibrium is reached.

Solution An iron block is dropped into water in an insulated tank. The final

temperature when thermal equilibrium is reached is to be determined.

Assumptions 1 Both water and the iron block are incompressible sub-

stances. 2 Constant specific heats at room temperature can be used for

water and the iron. 3 The system is stationary and thus the kinetic and

potential energy changes are zero, KE PE  0 and E U.

4 There are no electrical, shaft, or other forms of work involved. 5 The sys-

tem is well-insulated and thus there is no heat transfer.

Analysis We take the entire contents of the tank as the system(Fig. 4–35).

This is a closed systemsince no mass crosses the system boundary during

the process. We observe that the volume of a rigid tank is constant, and

thus there is no boundary work. The energy balance on the system can be

expressed as

Net energy transfer Change in internal, kinetic,

by heat, work, and mass potential, etc., energies

The total internal energy Uis an extensive property, and therefore it can be

expressed as the sum of the internal energies of the parts of the system.

Then the total internal energy change of the system becomes

The specific volume of liquid water at or about room temperature can be

taken to be 0.001 m^3 /kg. Then the mass of the water is

The specific heats of iron and liquid water are determined from Table A–3 to

be ciron0.45 kJ/kg · °C and cwater4.18 kJ/kg · °C. Substituting these val-

ues into the energy equation, we obtain

mwater

V

v



0.5 m^3

0.001 m 3 >kg

500 kg

3 mc 1 T 2 
T 124 iron 3 mc 1 T 2 
T 124 water 0

¢Usys¢Uiron¢Uwater 0

0 ¢U

Ein
Eout¬

¬

¢Esystem

WATER

25 °C

0.5 m^3

IRON

80 °C

m = 50 kg

FIGURE 4 –35

Schematic for Example 4 –12.

⎭⎪⎬⎪⎫ ⎭⎪⎬⎪⎫

Therefore, when thermal equilibrium is established, both the water and iron

will be at 25.6°C.

Discussion The small rise in water temperature is due to its large mass and

large specific heat.

T 2 25.6°C

1 50 kg 21 0.45 kJ>kg # °C 21 T 2
80°C 2  1 500 kg 21 4.18 kJ>kg # °C 21 T 2
25°C 2  0